After an hour of getting frustrated trying to get Apache on a remote server to behave as intended, I was as much confused as desperate.
I was sure everything is configured correctly, I cleared my browser cache, and eventually used a different browser, and still, I was getting the old website from my server, not the new.

I got the same result on my phone. So I tried a different approach. I switched to 3G and Whoa! The new website loaded O.o

I went back to the laptop, ran a wget on my website with --debug, and saw this cute line "X-CFLO-Cache-Result: TCP_HIT"

Since when do DSL providers employ such caches? :/ I got rid of the local cableguy to see the end of this nonsense! We don't even get to enjoy any speed benefits from it as my line is capped to 40 KB/s from 5 PM to 3 AM -_-
Try adding this to your .htaccess 
Header set Cache-Control "max-age=0, no-cache, no-store, must-revalidate"
Header set Pragma "no-cache"
and wget --no-cache --server-response http://mywebsite.com/mylink
I eventually removed etags and modified date, and added a reasonable expiration date. thanks :)
On chrome I think you can press ctrl+(reload button) to skip loading from isp cache.
@Georges00 Thats for local cache, they are talking about ISP level cache
haidcar wrote@Georges00 Thats for local cache, they are talking about ISP level cache
Some people suggested it for isp cache too when I was searching around.
ISP caching is becoming obsolete in the day of CDNs in many countries. If Cloudflare had a CDN in Lebanon for example, traffic from websites behind Cloudflare could be fetched locally by local ISPs and it wouldn't cost them international bandwidth.

The software ISPs use to cache content works only with http. With many websites moving to https, CDNs are more effective.